Following on from my post back in April when Copy project was first released: https://pwmather.wordpress.com/2020/04/29/projectfortheweb-copy-project-feature-workmanagement-taskmanagement-ppm-msproject-office365-ppm/, this feature was removed but has since been enabled again as seen below on one of my test Project for the web instances:
You will see the bubble notification appear to inform you of the new feature. Clicking the Project Name then the ellipsis you see the “Copy project” option:
Clicking this option loads the copied project and appends “- Copy” to the name. See below:
Original Project:
New Copy:
This process copies the tasks, the buckets and Project Name plus it also sets you as the Project Manager of the new copied project. Assignments and task progress is not copied – as you would expect. Here is a short video demonstrating this feature: https://youtu.be/xfYITKNaj7M
A handy feature for creating similar projects.
Modern Work Management - Project and the Power Platform blog 